**Electrostatics**

Physics requires practice to develop your solving problems
skills and your logical thinking . I strongly recommend to study carefully the
examples, and solve the following problems *in your
book.*

Problems: 2, 4, 5, 7, 8, 9, 10, 11, 12, 14, 16, 17, 21, 27, 35, 44, 47 Page 666

Exercises: 23.1 -23.8 Page 647

Problems

Electrostatics.

1. (1E) Two identical charges, each 8x10^{-5}
C, are separated by a distance of 25.0 cm. What is the force of repulsion?

2. (2E) The force of repulsion between two identical positive charges is 0.800 N when the charges are 0.100 m apart. Find the value of each charge.

3. (3E) A charge of + 3.0x10^{-6 }
C exerts a force of 940 N on a charge of + 6.0x10^{-6} C. How far apart
are the charges?

4. (5E) When a 9.0- mC charge is placed
0.12 cm from a charge *q * in a vacuum, the force between the two charges
is 850 N. What is the value of *q?*

5. (7E) Thee charges are located along the
*x- *axis. Charge ** A** (+3.00 m C) is located at the origin.
Charge

a) Find the total force (and direction) on charge *B.*

**b) **Find the total force (and direction) on charge *A.*

c) Find the total force (and direction) on charge **C.**

** **

6. (8E) Three charges are located along the
*x*-axis. Charge *A* ( +5.00 mC) is located at the origin. Charge *B
*( +4.50 mC) is located at *x *= +0.250 m. charge *C *(-4.20mC) is
located at *x *= + 0.650m. Find the total force (and direction on charge
*B.*

7.
(22G).
A charge *Q* is transferred from an initially uncharged plastic ball to an
identical ball 12 cm away. The force of attraction is then 17 mN. How many
electrons were transferred from one ball to the other?

8.
(2G)**.** How many
electrons make up a charge of - 30
μF.

9.
(10G)**.****
**Compare the electric force holding
the electron in orbit r = 0.53 x 10^{-10} m
around
the proton nucleus of the hydrogen atom, with the gravitational force between
the same electron and proton. What is the ratio of these two forces?

10.
(12G)**.**
Particles of charge μC are
placed in a line . The center one is 0.35 m from each of the others. Calculate
the net force on each charge due to the other two.

11.
(17G)**.**
Three charged particles are placed at the corners of an equilateral triangle of
side 1.20 m . The charges are +4.0 μC, +8.0
μC
and
μC . Calculate
the magnitude and direction of the net force on each due to the other two.

12.
(20G)**.**
A μC
and
a μC
charge
are placed 18.5 cm apart. Where can a third charge be placed so that it
experiences no net force?

13.
(22G)**.**
A charge *Q* is transferred from an initially uncharged plastic ball to an
identical ball 12 cm away. The force of attraction is then 17 mN. How many
electrons were transferred from one ball to the other?

14.
(4S)**.
**Two protons in an atomic nucleus are
typically separated by a distance of 2 Χ 10^{15}
m. The electric repulsion force between the protons is huge, but the attractive
nuclear force is even stronger and keeps the nucleus from bursting apart. What
is the magnitude of the electric force between two protons separated by 2.00 Χ
10^{15}
m? ** **

** **

15.
(5S)**.** Two protons in a molecule are
separated by 3.80 Χ 10^{10}
m. Find the electric force exerted by one proton on the other. (b) How does the
magnitude of this force compare to the magnitude of the gravitational force
between the two protons? (c) **What If? **What must be the charge-to-mass
ratio of a particle if the magnitude of the gravitational force between two of
these particles equals the magnitude of electric force between them? **
( mp = 1.67 10 ^{-27} kg)**

16.
(7S). Three point charges
are located at the corners of an equilateral triangle as shown in Figure P23.7.
Calculate the resultant electric force on the 7.00-*μ*C charge.

17.
(9S)**.****
**Two identical conducting small spheres are
placed with their centers 0.300 m apart. One is given a charge of 12.0 nC and
the other a charge of 18.0 nC. (a) Find the electric force exerted by one
sphere on the other. (b) **What If? **The spheres are connected by a
conducting wire. Find the electric force between the two after they have come to
equilibrium. ** **

** **

18. (11S)**.****
**In the Bohr
theory of the hydrogen atom, an electron moves in a circular orbit about a
proton, where the radius of the orbit is 0.529 Χ 10^{10} m. (a) Find
the electric force between the two. (b) If this force causes the centripetal
acceleration of the electron, what is the speed of the electron?

19. (10S)**
**Two
identical particles, each having charge +*q*, are fixed in space and
separated by a distance *d*. A third point charge *Q *is free to move
and lies initially at rest on the perpendicular bisector of the two fixed
charges a distance *x *from the midpoint between the two fixed charges
(Fig. P23.12). (a) Show that if *x *is small compared with *d*, the
motion of *Q *will be simple harmonic along the perpendicular bisector.
Determine the period of that motion. (b) How fast will the charge *Q *be
moving when it is at the midpoint between the two fixed charges, if initially it
is released at a distance *a *<< *d* from the midpoint?

* *** **

20. (12S) Determine the point (other than infinity) at which the electric field is zero.

21. (14S)**
**Three charges are at the corners of an
equilateral triangle as shown in Figure P23.7. (a) Calculate the electric field
at the position of the 2.00-*μ*C charge due to the 7.00-*μ*C and
4.00-*μ*C charges. (b) Use your answer to part (a) to determine the force
on the 2.00-*μ*C charge.

22. (19S)**
**Three point charges are arranged as shown.
(a) Find the vector electric field that the 6.00-nC and 3.00-nC charges
together create at the origin. (b) Find the vector force on the 5.00-nC charge.

23. (16S)**
**Two 2.00-*μ*C point charges are
located on the *x *axis. One is at *x *= 1.00 m, and the other is at
*x *= 1.00 m. (a) Determine the electric field on the *y *axis at *
y *= 0.500 m. (b) Calculate the electric force on a 3.00-*μ*C charge
placed on the *y *axis at *y *= 0.500 m.

24. (17S)**
**Four point charges are at the corners of a
square of side *a *as shown. (a) Determine the magnitude and direction of
the electric field at the location of charge *q*. (b) What is the resultant
force on *q*?

**Electric field**

** **

25. (25G) A downward force of 8.4 N is exerted on a - 8.8 μC charge. What are the magnitude and direction of the electric field at this point?

26**.
****
(**28G)
What are the magnitude and direction of the electric field at a point midway
between a - 8.0 μC
and
a +7.0 μC
charge
8.0 cm apart? Assume no other charges are nearby.

27. (33G) Calculate the electric field at the center of a square 52.5 cm on a side if one corner is occupied by a + 45.0 μC charge and the other three are occupied by - 27.0μC charges.

28.
(34G)
Calculate the electric field at one corner of a square 1.00 m on a side if the
other three corners are occupied by 2.25x 10^{-6 C }
charges.

29.
(36G)
Two point charges, Q_{1} =
25μC and
Q_{2} = 50 μC
are
separated by a distance of 12 cm. The electric field at the point P is zero. How far from Q_{1 }
is
P?

**Gauss.**

30.
(43G)
The total electric flux from a cubical box 28.0 cm on a side is
1.45x 10^{3}
N.m^{2} /C .What
charge is enclosed by the box?

31.(45G)
Two objects, have
charges μC and
μC
respectively,
and a third object, is
electrically neutral. (*a*) What is the electric flux through the surface
A_{1} that
encloses all three objects? (*b*) What is the electric flux through the
surface
A_{2} that
encloses the third object only?

32.
(49G)
A solid metal sphere of radius 3.00 m carries a total charge of
μC.What
is the magnitude of the electric field at a distance from the spheres center of
(*a*) 0.15 m, (*b*) 2.90 m, (*c*) 3.10 m, and (*d*) 6.00 m?
(*e*) How would the answers differ if the sphere were a thin shell?

33.
(11S)**
**Four closed surfaces, *S*_{1}
through *S*_{4}, together with the charges 2*Q*, *Q*,
and *Q *are sketched in Figure P24.11. (The colored lines are the
intersections of the surfaces with the page.) Find the electric flux through
each surface.

** **

** **34.
(24S) A solid sphere of
radius 40.0 cm has a total positive charge of 26.0 *μ*C uniformly
distributed throughout its volume. Calculate the magnitude of the electric field
(a) 0 cm, (b) 10.0 cm, (c) 40.0 cm, and (d) 60.0 cm from the center of the
sphere.

35. (26S)**
**A cylindrical shell of radius 7.00 cm and
length 240 cm has its charge uniformly distributed on its curved surface. The
magnitude of the electric field at a point 19.0 cm radially outward from its
axis (measured from the midpoint of the shell) is 36.0 kN/C. Find (a) the net
charge on the shell and (b) the electric field at a point 4.00 cm from the axis,
measured radially outward from the midpoint of the shell.

36. (29S)Consider
a long cylindrical charge distribution of radius *R *with a uniform charge
density *ρ*. Find the electric field at distance *r *from the axis
where *r *<* R. *

** **

37. (31S)Consider
a thin spherical shell of radius 14.0 cm with a total charge of 32.0 *μ*C
distributed uniformly on its surface. Find the electric field (a) 10.0 cm and
(b) 20.0 cm from the center of the charge distribution.

** **

38.(36S)**
**An insulating sphere is 8.00 cm in diameter
and carries a 5.70-*μ*C charge uniformly distributed throughout its
interior volume. Calculate the charge enclosed by a concentric spherical surface
with radius (a) *r *= 2.00 cm and (b) *r *= 6.00 cm.

39. (39S). A long, straight metal rod has a radius of 5.00 cm and a charge per unit length of 30.0 nC/m. Find the electric field (a) 3.00 cm, (b) 10.0 cm, and (c) 100 cm from the axis of the rod, where distances are measured perpendicular to the rod.

** **

40. (44S)** **
A solid conducting sphere of radius 2.00 cm has a
charge of 8.00 *μ*C. A conducting spherical shell of inner radius4.00 cm
and outer radius 5.00 cm is concentric with the solid sphere and has a total
charge of 4.00 *μ*C. Find the electric field at (a) *r *= 1.00 cm,
(b) *r *= 3.00 cm, (c) *r *= 4.50 cm, and (d) *r *= 7.00 cm from
the center of this charge configuration.